Like some others who have commented, I'm not sure it's actually that typical for adults to have opposite-sex close friends, much less to call them by some kind of pet name.
'Mate' is BE, but the AE equivalents 'pal' or 'bud' are similar in that they're also used between men who are complete strangers, as when complaining of a bad driver, similar to 'Freundchen.' So, 'He's my best pal / best buddy' would work, but in direct address, no, not so much.
There are some terms that seem to be used in certain circles in younger generations, like 'bae' or 'bestie.' I've never heard anyone actually use those in real Iife, but they show up in crosswords.
A woman might call a man 'babe' or 'hon,' and vice versa. That would be used between spouses or romantic partners, but it could also be between good friends.
'Love' or 'luv' in this sense is mainly BE, and at least some AE speakers are likely to find it annoying, overly familiar, from strangers in customer-service jobs. The AE equivalents 'sweetie' or 'honey' can come across as quite condescending, so politer employees stick with 'ma'am' and 'sir.'
'Sweetheart,' 'honey,' etc. are mainly used either between spouses or to children. 'Darling' is similar, but my impression is that it's more old-fashioned or BE.
'Pumpkin' or 'punkin' in AE is used only toward young children in my experience, and perhaps in some regions more than others; I would have guessed it was mainly southern.